Polar Decomposition of Complexified Quaternions and Octonions
Advances in Applied Clifford Algebras(2020)
摘要
We present a hitherto unknown polar representation of complexified quaternions (also known as biquaternions), also applicable to complexified octonions. The complexified quaternion is factored into the product of two exponentials, one trigonometric or circular, and one hyperbolic. The trigonometric exponential is a real quaternion, the hyperbolic exponential has a real scalar part and imaginary vector part. This factorisation is shown to be isomorphic to the polar decomposition of linear algebra.
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关键词
Biquaternion,Quaternion,Polar decomposition
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